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Can somebody please go through the steps of solving this:

$$ \frac{1}{2} x^{-1/2} = \frac{1}{8} $$

The calculator says it's 16 but I keep getting the following answer:

$$ \frac{1}{16}\ $$


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I took the liberty of rewriting your equation using the easier to read MathJax formula. Is this what you meant?

1 Answer

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To solve the following equation for x:

$$ \frac{1}{2} x^{-1/2} = \frac{1}{8} $$

Steps:

  1. Multiply both sides of the equation by 2 to remove the 1/2 in front of the x. This gives us:

$$ \frac{1}{2} x^{-1/2} * 2 = \frac{1}{8} * 2 $$

  1. Simplify it (because 1/2 * 2 = 1 and 1/8 * 2 = 1/4):

$$ x^{-1/2} = \frac{1}{4} $$

  1. Now to solve x for a negative index, a negative index implies 1/x. Basically flip both sides. In general, the following equation is true for negative indicies:

Negative Indices Rule

So, therefore, it becomes:

$$ x^{1/2} = 4 $$

  1. Now to solve for x where x^(1/2) = 4 - we can square both sides of the equation to remove the ^(1/2). Hence, we get:

$$ x = 16 $$

Hope that helps. Let me know if you require any additional clarification.


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